Z Transform Filters Introduction.
In the same way that analog filters can be designed by placement
of poles and zeros in the s plane, then digital filters can also
be designed by suitable location of poles and/or zeros in the
Z plane. Digital filters are often categorised as finite
impulse response(FIR) and infinite impulse response(IIR).
Finite impulse response filters can be implemented with
zeros and IIR filters with poles and zeros.
Software packages are available for the design of FIR
filters and IIR filters can be designed by sampled
approximations to classical analog responses.
Here we look at some simple filters to illustrate some
of their properties and some of the basic concepts used
in the design, eg simple pole-zero configurations, some
named filters (allpass, linear phase, comd etc), sampled
approximations to analog designs, FFT and frequency sampling
Definitions of Low pass, High pass and Band pass filters,
indicated above, have
to be modified when referring to digital filters because of the
periodicity of their responses. LP, HP and BP filters now
refer to the frequency interval from 0 to half the sampling
frequency instead from 0 to infinity. The spectra of digital filters are periodic with a period of ws.
If a filter has 2 CC zeros shown by the 2 black o's above and
2 CC poles shown by the black x's above then the magnitude and
phase of the response at w is given by
Mag = (a1 ´ a2)/
(b1 ´ b2)
and Phase =
(q1 + q2) - (q3 + q4).
a1, a2 are the distances from the zeros to the point which subtends wT at the center. (T =
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© 2000 Cuthbert A. Nyack.